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© Kompilation durch diese Firma

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Datei: TestPosition.vdmrt   Sprache: Lisp

Untersuchung PVS©
(complete_product
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          (("1" (split)
            (("1" (flatten)
              (("1"
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                (("1" (replace -2)
                  (("1" (hide -2)
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                      (("1" (assert)
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       ("3" (typepred "d0")
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              (("3" (expand "metric_triangle?")
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                      (("3" (hide-all-but (-3 -6 1))
                        (("3" (rewrite "sq_le" 1 :dir rl)
                          (("3" (rewrite "sq_sqrt")
                            (("3" (rewrite "sq_plus")
                              (("3"
                                (rewrite "sq_le" -1 :dir rl)
                                (("3"
                                  (rewrite "sq_le" -2 :dir rl)
                                  (("3"
                                    (assert)
                                    (("3"
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                                      (("3"
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                                        (("3"
                                          (assert)
                                          (("3"
                                            (name-replace
                                             "D1_XZ"
                                             "d1(x!1`2, z!1`2)")
                                            (("3"
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                                               "d0(x!1`1, z!1`1)")
                                              (("3"
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                                                  (("3"
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                                                     "d1(y!1`2, z!1`2)")
                                                    (("3"
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                                                       "D0_YZ"
                                                       "d0(y!1`1, z!1`1)")
                                                      (("3"
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                                                        (("1"
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                                                           -1
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                                                            (lemma
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                                                             ("a"
                                                              "D1_XY"
                                                              "c"
                                                              "D1_YZ"
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                                                              "D0_XY"
                                                              "d"
                                                              "D0_YZ"))
                                                            (("2"
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   ((real_ge_is_total_order name-judgement "(total_order?[real])"
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    (sqrt_sq formula-decl nil sqrt "reals/")
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    (real nonempty-type-from-decl nil reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sq const-decl "nonneg_real" sq "reals/")
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    (sq_le formula-decl nil sq "reals/")
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    (real_le_is_total_order name-judgement "(total_order?[real])"
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    (sq_plus formula-decl nil sq "reals/")
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
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    (<= const-decl "bool" reals nil)
    (sq_sqrt formula-decl nil sqrt "reals/")
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    (metric? const-decl "bool" metric_def nil))
   nil))
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                                                       :dir
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                                                      (("1"
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                                                         "sq_lt"
                                                         -2
                                                         :dir
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                                                        (("1"
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                                                          (("1"
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                                                             -1
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                                                              (("1"
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                                                                 1
                                                                 :dir
                                                                 rl)
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                                                                  (assert)
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                   ("2" (hide-all-but (-2 1))
                    (("2" (expand "cauchy?")
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                                          (("2"
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                                             "sq_lt"
                                             -3
                                             :dir
                                             rl)
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                  (("2" (expand "cauchy?")
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        nil))
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    nil)
   ((fullset const-decl "set" sets nil)
    (metric_convergent? const-decl "bool" metric_space_def nil)
    (nonneg_rat_max application-judgement
     "{s: nonneg_rat | s >= q AND s >= r}" real_defs nil)
    (nat_max application-judgement "{k: nat | i <= k AND j <= k}"
     real_defs nil)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (member const-decl "bool" sets nil)
    (d1 formal-const-decl "metric[T1]" complete_product nil)
    (metric nonempty-type-eq-decl nil metric_def nil)
    (metric? const-decl "bool" metric_def nil)
    (nnreal type-eq-decl nil real_types nil)
    (sq_lt formula-decl nil sq "reals/")
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (sq_div formula-decl nil sq "reals/")
    (sq_sqrt formula-decl nil sqrt "reals/")
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sqrt const-decl "{nnz: nnreal | nnz * nnz = nnx}" sqrt "reals/")
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (d0 formal-const-decl "metric[T0]" complete_product nil)
    (ball const-decl "set[T]" metric_space_def nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (metric_converges_to const-decl "bool" metric_space_def nil)
    (cauchy? const-decl "bool" metric_space_def nil)
    (T1 formal-type-decl nil complete_product nil)
    (sequence type-eq-decl nil sequences nil)
    (TRUE const-decl "bool" booleans nil)
    (T0 formal-type-decl nil complete_product nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (metric_complete? const-decl "bool" metric_space_def nil))
   shostak)))


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